Second-order teleparallel gauge theory

Abstract

In this work, we analyze second-order extensions of teleparallel theories of gravity as gauge theories for the translation group. We use Utiyama’s approach to gauge theories and show that it is possible to include second-order derivative terms in the Lagrangian of the gauge potential and preserve gauge invariance. Besides the usual field strength, a new object has to be introduced in order to preserve both gauge and diffeomorphism invariances. From this new object, we obtain a set of fourteen independent invariants which leads to equations that are linear in the fourth derivative of the tetrad field. We analyze a particular example with one of these invariants and evaluate the weak field limit, showing that the effective gravitational potential is a combination of Newton and Yukawa potentials.

Scalar-multi-tensor approach to fT,B,∇μT,∇μB teleparallel gravity

“…In the first works by Utiyama and Kibble [96,97] on gravitation as a gauge theory, the spin connection is the gauge field that is introduced to recover the invariance by local Lorentz transformations. The teleparallel theory referred to in this paper is built from the perspective of a gauge theory associated to the translation group, as elucidated in [98]. This means that the Lorentz transformations are only considered here as a global symmetry.…”